Cosmological lensing as a jump process
Abstract
We develop a jump-process formalism for the probability density function (PDF) of gravitational lensing fields. In the Born approximation, each lens adds a jump to the convergence κ and the two components of the shear, making lensing a jump process in redshift. For independent lenses, the joint PDF of the lensing fields obeys a compensated Kolmogorov-Feller equation, which we solve in closed form in Fourier space and extend to clustered lenses using their two-point correlation function. A Fourier-Hankel inversion then yields the joint PDF of κ and the shear magnitude γ, from which the magnification PDF follows, including its high-magnification tail, without sampling noise. We use these PDFs to train an updated version of the FLUMEN emulator, which makes likelihood-based inference from the full magnification distribution feasible across cosmologies. To motivate such analyses, we estimate that samples of 104 Roman supernovae, 105 Rubin supernovae, 300 Einstein Telescope standard sirens, and 12 LISA standard sirens could constrain the matter fluctuation amplitude σ8 respectively to 4.8\%, 5.1\%, 8.5\%, and 19\%, with the other cosmological parameters fixed.
Related
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BibTeX
@misc{baltabay2026cosmological,
title = {{Cosmological lensing as a jump process}},
author = {Galymzhan Baltabay and Ville Vaskonen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40341},
eprint = {2610.40341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40341},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cosmological lensing as a jump process
AU - Galymzhan Baltabay
AU - Ville Vaskonen
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40341
UR - https://arxiv.org/abs/2610.40341
AB - We develop a jump-process formalism for the probability density function (PDF) of gravitational lensing fields. In the Born approximation, each lens adds a jump to the convergence κ and the two components of the shear, making lensing a jump process in redshift. For independent lenses, the joint PDF of the lensing fields obeys a compensated Kolmogorov-Feller equation, which we solve in closed form in Fourier space and extend to clustered lenses using their two-point correlation function. A Fourier-Hankel inversion then yields the joint PDF of κ and the shear magnitude γ, from which the magnification PDF follows, including its high-magnification tail, without sampling noise. We use these PDFs to train an updated version of the FLUMEN emulator, which makes likelihood-based inference from the full magnification distribution feasible across cosmologies. To motivate such analyses, we estimate that samples of 10^4 Roman supernovae, 10^5 Rubin supernovae, 300 Einstein Telescope standard sirens, and 12 LISA standard sirens could constrain the matter fluctuation amplitude σ_8 respectively to 4.8\%, 5.1\%, 8.5\%, and 19\%, with the other cosmological parameters fixed.
ER -